With many measurements available from our sensors (though not necessarily ones that achieve Whitney's results), the problem that remains is to properly choose them so that nonlinear reconstruction is possible and robust to noise.
While nonlinear reconstruction has proved to be extremely advantageous, the overwhelming majority of sensor placement and feature selection methods rely on measures of linear or Gaussian reconstruction accuracy as an optimization criteria.
Such methods include techniques based on sampling modal bases [1]}, [2]}, [3]}, [4]}, [5]}, linear dynamical system models [6]}, [7]}, [8]}, [9]}, [10]}, Bayesian and maximum likelihood optimality in linear inverse problems [11]}, [12]}, [13]}, information-theoretic criteria under Gaussian or other simple statistical models [14]}, [15]}, [16]}, [17]}, [18]}, and sparse linear approximation in dictionaries using LASSO [19]}, [20]} or orthogonal matching pursuit [21]}, [22]}.
We provide an overview of a representative collection of these methods that we shall use as a basis for comparison in Section .
